A New Interface Method for Hyperbolic Problems with Discontinuous Coefficients: One-Dimensional Acoustic Example

Journal of Computational Physics

Volumn 168, Issue 1, 2001, Pages 227-248

  Piraux, Joël ^a   Lombard, Bruno ^a  

^a LABORATOIRE DE MÉCANIQUE ET D ACOUSTIQUE   (France)

Author keywords

Acoustics; Discontinuous coefficients; Heterogeneous media; Interface methods; Lax Wendroff, TVD, and WENO schemes

Indexed keywords

NUMERICAL METHODS;

DISCONTINUOUS COEFFICIENTS; FIRST ORDER; HETEROGENEOUS MEDIA; HYPERBOLIC PROBLEMS; INTERFACE METHOD; LAX-WENDROFF SCHEME; LINEAR HYPERBOLIC SYSTEMS; ONE-DIMENSIONAL; TVD SCHEME; WENO SCHEMES;

ACOUSTIC WAVE PROPAGATION;

EID: 0042323064     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1006/jcph.2001.6696     Document Type: Article

References (16)

1. L. M. Brekhovskikh, Waves in Layered Media (Academic Press, New York, 1980).
2. D. Calhoun, A Cartesian Grid Method for Solving the Streamfunction Vorticity Equations in Irregular Geometries, Ph.D. thesis (University of Washington, 1999), available at ftp://amath.washington. edu/pub/calhoun/thesis/thesis.ps.gz.
3. F. Collino, P. Joly, and F. Millot, Fictitious domain method for unsteady problems: Application to electromagnetic scattering, J. Comput. Phys. 138, 907 (1997).
4. R. P. Fedkiw, B. Merriman, R. Donat, and S. Osher, The Penultimate Scheme for Systems of Conservation Laws: Finite Difference ENO with Marquina's Flux Splitting, Preprint, available at ftp://ftp.math.ucla.edu/pub/camreport/cam96-18.ps.gz.
5. T. Fogarty, High-Resolution Finite Volume Methods for Acoustics in a Rapidly-Varying Heterogeneous Medium, Master's thesis (University of Washington, 1997), available at ftp://amath.washington. edu/pub/rjl/students/fogarty:masters.ps.gz.
6. T. R. Fogarty and R. J. LeVeque, High-resolution finite volume methods for acoustic waves in periodic and random media, J. Acoust. Soc. Am. 1(106), 17 (1999).
7. E. Godlewski and P. A. Raviart, Numerical Approximation of Hyperbolic Systems of Conservation Laws (Springer-Verlag, Berlin/New York, 1996).
8. G. S. Jiang and C. W. Shu, Efficient implementation of weighted ENO schemes, J. Comput. Phys. 126, 202 (1996).
9. J. O. Langseth and R. J. LeVeque, A wave-propagation method for three-dimensional hyperbolic conservation laws, J. Comput. Phys., in press, available at ftp://amath.washington.edu/pub/rjl/papers/ jol-rjl:3d.ps.Z.
10. R. J. LeVeque, Numerical Methods for Conservation Laws (Birkhäuser, Basel, 1990).
11. R. J. LeVeque, Wave propagation algorithms for multi-dimensionnal hyperbolic systems, J. Comput. Phys. 131(2), 327 (1997).
12. Z. Li. The Immersed Interface Method - A Numerical Approach for Partial Differential Equations with Interfaces, Ph.D. thesis (University of Washington, 1994), available at ftp://ftp.math.ucla.edu/pub/ zhilin/Papers/thesis.ps.Z.
13. S. I. Rokhlin and Y. J. Wang, Analysis of boundary conditions for elastic wave interaction with an interface betwween two solids, J. Acoust. Soc. Am. 89(2), 503 (1991).
14. A. Wiegmann, The Explicit Jump Immersed Interface Method and Interface Problems for Differential Equations, Ph.D. thesis (University of Washington, 1998).
15. C. Zhang, Immersed Interface Method for Hyperbolic Systems of Partial Differential Equations with Discontinuous Coefficients, Ph.D. thesis (University of Washington, 1996), available at ftp://amath.washington.edu/pub/chaoming/dissertation.ps.Z.
16. C. Zhang and R. J. LeVeque, The immersed interface method for acoustic wave equations with discontinuous coefficients, Wave Motion 25(3), 237 (1997).